The percentage would be 4% because you have to subtract 20 from 16 to find the percentage and that would be 4. :D
Hope this helped. :D<span />
Answer:
radius i think
Step-by-step explanation:
Here is the correct computation of the question.
The future lifetimes (in months) of two components of a machine have the following joint density function:
for 0 < x < 50 - y < 50, otherwise.
Write down a single integral representing the probability that both components are still functioning in 20 months from now.
Answer:
![\mathbf{ P{(x>20) \cap(Y>20)} } =0.0008}](https://tex.z-dn.net/?f=%5Cmathbf%7B%20P%7B%28x%3E20%29%20%5Ccap%28Y%3E20%29%7D%20%7D%20%3D0.0008%7D)
Step-by-step explanation:
From the given information;
for 0 < x < 50 - y < 50, otherwise.
We can assert that the probability is the integral of the given density over the part of the range 0 ≤ x ≤ 50 - y ≤ 50 in which both x and y are greater than 20.
From the attached file below; their shows a probability density graph illustrating the above statement being said.
Now; to determine the probability that illustrates the integral of the density ; we have : P[(X > 20)∩(Y > 20)]
In addition to that:
From the image attached below;
We look into the region where the joint density under study is said to be positive and the triangle limits by the line axis x+y = 50
∴
![P{(x>20) \cap(Y>20)} } = \dfrac{6}{125000}\int\limits^{30}_{20}\int\limits^{50-x}_{20}(50-x-y)dydx](https://tex.z-dn.net/?f=P%7B%28x%3E20%29%20%5Ccap%28Y%3E20%29%7D%20%7D%20%3D%20%5Cdfrac%7B6%7D%7B125000%7D%5Cint%5Climits%5E%7B30%7D_%7B20%7D%5Cint%5Climits%5E%7B50-x%7D_%7B20%7D%2850-x-y%29dydx)
![P{(x>20) \cap(Y>20)} } = \dfrac{6}{125000}\int\limits^{30}_{20} \dfrac{1}{2}(x-30^2)dx](https://tex.z-dn.net/?f=P%7B%28x%3E20%29%20%5Ccap%28Y%3E20%29%7D%20%7D%20%3D%20%5Cdfrac%7B6%7D%7B125000%7D%5Cint%5Climits%5E%7B30%7D_%7B20%7D%20%5Cdfrac%7B1%7D%7B2%7D%28x-30%5E2%29dx)
![P{(x>20) \cap(Y>20)} } = \dfrac{6}{125000} ( \, \dfrac {500}{3})](https://tex.z-dn.net/?f=P%7B%28x%3E20%29%20%5Ccap%28Y%3E20%29%7D%20%7D%20%3D%20%5Cdfrac%7B6%7D%7B125000%7D%20%28%20%5C%2C%20%5Cdfrac%20%7B500%7D%7B3%7D%29)
![P{(x>20) \cap(Y>20)} } = \dfrac{6*500}{125000*3}](https://tex.z-dn.net/?f=P%7B%28x%3E20%29%20%5Ccap%28Y%3E20%29%7D%20%7D%20%3D%20%5Cdfrac%7B6%2A500%7D%7B125000%2A3%7D)
![P{(x>20) \cap(Y>20)} } = \dfrac{3000}{375000}](https://tex.z-dn.net/?f=P%7B%28x%3E20%29%20%5Ccap%28Y%3E20%29%7D%20%7D%20%3D%20%5Cdfrac%7B3000%7D%7B375000%7D)
![\mathbf{ P{(x>20) \cap(Y>20)} } =0.0008}](https://tex.z-dn.net/?f=%5Cmathbf%7B%20P%7B%28x%3E20%29%20%5Ccap%28Y%3E20%29%7D%20%7D%20%3D0.0008%7D)
Thus; the single integral representing the probability that both components are still functioning in 20 months from now is ![\mathbf{ P{(x>20) \cap(Y>20)} } =0.0008}](https://tex.z-dn.net/?f=%5Cmathbf%7B%20P%7B%28x%3E20%29%20%5Ccap%28Y%3E20%29%7D%20%7D%20%3D0.0008%7D)
Answer:
it would be 25%
there is only one number that is greater than 6
Answer:
: 1
Step-by-step explanation:
they are both divisible by 4 so you divide. You will get 4:3. Since you wanted n:1 , you have to divide both sides by 3. the answer is
: 1
If this helped, please mark me as brainliest, thank you!